Consider the following statements: 1. In a triangle ABC, if cotA·cotB·cotC > 0, then the triangle is an acute angled triangle. 2. In a triangle ABC, if tanA·tanB·tanC > 0, then the triangle is an obtuse angled triangle. Which of the statements given above is/are correct?

Statement 1: In a triangle, A + B + C = π. cotA·cotB·cotC > 0 requires either all three cotangents positive (all angles acute) or exactly two negative (two obtuse angles), but a triangle cannot have two obtuse angles. So all three angles must be acute — the triangle is acute angled. Statement 1 is correct. Statement 2: In any triangle, tanA + tanB + tanC = tanA·tanB·tanC. For an acute triangle, all tangents are positive, so the product is also positive. Thus tanA·tanB·tanC > 0 occurs in acute triangles too, not only obtuse ones. Statement 2 is incorrect.